Students will not see this notation during the activity portion of the lesson but the margin notes will provide this formalization.ĭuring the activity, point out the repetitive nature of their work, adding many terms that all consist of a height and a width. Instead, we are using informal summation notation by referring to the rectangles from 1 to n, the height of the ith rectangle (f(xi)) and the width of each rectangle, which we are for now assuming is uniform and we are calling ∆x.
Summation notation is notoriously hard for students so at this point in the unit, we have chosen to hold off on the formal notation that uses the index of summation to arrive at the left, right, or midpoint of each interval. After exploring Riemann sum approximations with more and more rectangles, students explore the idea of infinitely many rectangles giving an exact area under a curve. In this lesson students are first introduced to the integral and its notation.
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